A bot is a software application that runs automated tasks (e.g., scripts) over the Internet. Bots perform malicious tasks like skewing website statistics, price scraping, spam distribution, DOS attack, etc. Single bots usually request network resources at a much higher rate than human users, which can effect load on the server and response times for human users.
A botnet is a group of computers connected in a coordinated fashion. Individual computers of a large-scale botnet might request resources at a human-like speed, but together they place a heavy load on the servers and, therefore, can cause a server to go down.